Why is an Acoustic Guitar so much LOUDER than an Electric Guitar?

[The Observer]

Mile High,

The problem here is you are not putting a number on the waves that are "1000 times larger."  Larger than what?  How large are they?

1000 times larger than the waves coming from the string on the electric guitar.

The Observer

[MileHigh]

The Observer:

1000 times larger than the waves coming from the string on the electric guitar.

Suppose the average audio power coming from the electric guitar string is 1 microwatt.  That means that the acoustic guitar string is 1000 times that, which is 1 milliwatt.  Then using my example the average strumming power is 20 times that, which is 20 milliwatts.

So there is your breakdown, each type of guitar is turning a fraction of the average strumming power into audio power.   The acoustic guitar can turn 5% of the strumming power into audio power, whereas the electric guitar can only turn 0.005% of the strumming power into audio power.

That's it, there are no gains or amplification when you compare an acoustic guitar to an electric guitar.  There is no real relationship between the two devices, they just have different stats.  Both convert mechanical strumming power into audio power, and the acoustic guitar does a better job at it.

MileHigh

[The Observer]

Mile High,

You say that there is a lot of energy in the strum that is never realized as sound.
And that the Acoustic Cavity somehow \taps into more of it.
 
    If you can tap that energy any other way than with resonance...  OK you got me !

Once more...you state sound is not amplified.

I bet if you heard sound waves coming from an electric amplifier 30 Db louder...
                                                                          you would say that sound was amplified.

       Curious that the sound box of the guitar would skew your judgment that sound is being amplified by it.

The Observer                         

[MileHigh]

Hey Observer,

It sounds like you are getting my points which is cool.

Curious that the sound box of the guitar would skew your judgment that sound is being amplified by it.

The fact that the ears are very sensitive to sound energy and the sound box allows for more efficient extraction of the available energy in the vibrating string is a happy combination that makes acoustic guitars just fine for sing-alongs.  If the sound box wasn't there (electric guitar) then much more of the available string energy goes into heat production.

There is the concept of "impedance matching" that plays an important part here that was not discussed.  The sound box facilitates an impedance match between the vibrating string energy and the transformation and export of that energy into acoustic energy that goes into the surrounding environment.  You can't "over impedance match" to get any extra energy.  However, with a good impedance match between the vibrating string and the air (super-duper sound box) you can get "a bigger slice of the energy pie" that is represented by the vibrating string.  There are still heat slices, but at least the audio slice gets larger and the heat slices get smaller.

MileHigh

[The Observer]

Mile High,

Impedence Matching?

Let's call it what it is....    Forced Resonance.

     The String causes Waves in the air...

     The Waves in the air are what forces the air in the Helmholtz Chamber into resonance.
     The Resonant Chamber stores Energy.
     The Resonant Chamber Vibrates with an amplitude congruent to the energy it can store.
     The Resonant Chamber emits a Wave congruent to the energy it can store.

     The Wave emitted from the Chamber is larger than the original wave.
     The very definition of amplification.

This is how it it working... is it not?

The Observer